T. E. Raptis

T. E. Raptis

Some preliminary results are reported on the equivalence of any n-queens problem with the roots of a Boolean valued quadratic form via a generic dimensional reduction scheme. It is then proven that the solutions set is encoded in the entries of a special matrix. Further examination reveals a direct association with pointwise Boolean fractal operators applied on certain integer sequences associated with this matrix suggesting the presence of an underlying special geometry of the solutions set.

T. E. Raptis

The interactive computation paradigm is reviewed and a particular example is extended to form the stochastic analog of a computational process via a transcription of a minimal Turing Machine into an equivalent asynchronous Cellular Automaton with an exponential waiting times distribution of effective transitions. Furthermore, a special toolbox for analytic derivation of recursive relations of important statistical and other quantities is introduced in the form of an Inductive Combinatorial Hierarchy.